Modeling Interactions
between the
Magnetosphere, Ionosphere
&
Thermosphere
M.Wiltberger
NCAR/HAO
Outline
• Overview of MIT ‘circuit’
• Modeling Magnetospheric impacts on the Ionosphere
– Energetic Particle Fluxes
• Modeling Thermospheric impacts on the Ionosphere
– Neutral Wind Driven Currents
• Modeling Ionospheric impacts on the Magnetosphere
– Ion Outflow
• Conclusions
• References
Magnetospheric Currents
Dayside and
R1 Currents
Ring and R2 Currents
Neutral Sheet Current
• Magnetopause current systems are created by the force
balance between the Earth’s dipole and the incoming
solar wind
Ionospheric Currents
Region 1
Region 2
• FAC from the magnetosphere close though
Pedersen and Hall Currents in the ionosphere
MI Coupling Eqs
• As described in Kelly [1989] The fundamental equation for MI
coupling is obtain by breaking the ionospheric current into
parallel and perpendicular components and requiring continuity
∇i J = ∇ ⊥ i J ⊥ +
∂J
∂s
=0
• Assuming no current flows out the bottom of the ionosphere we
get
J =
∫ (∇
⊥
i J ⊥ ) ds
∆s
• Further assuming the electric field is uniform with height we get
(
J = ∇ ⊥ i Σ i EI
)
• And finally using and electrostatic approximation in the MI
coupling region we obtain
(
J = −∇ ⊥ i Σi∇ ⊥ Φ
)
Conductances from Particle Flux
• Spiro et al. [1982] used Atmospheric Explorer observations
to determine a set of empirical relationships between the
average electron energy and the electron energy flux
⎛ 20 E0 ⎞ 0.5
ΣP = ⎜
φ
2 ⎟
⎝ 4 + E0 ⎠
Σ H = E 0.625Σ P
• Robinson et al. [1987] revised the relationships using Hilat
data and careful consideration of Maxwellian used to
determine the average energy
⎛ 40 E0 ⎞ 0.5
ΣP = ⎜
φ
2 ⎟
⎝ 16 + E0 ⎠
Σ H = 0.45 E 0.85Σ P
• Hardy et al. [1987] reports a slightly mistaken version of
the Robinson et al. revision of the Spiro’s results
⎛ 40 E0 ⎞ 0.5
ΣP = ⎜
φ
2 ⎟
⎝ 16 + E0 ⎠
Σ H = 0.45E 0.625Σ P
Calculation of Particle Fluxes
• Empirical relationships are used to convert MHD
parameters into a characteristic energy and flux of the
precipitating electrons
– Initial flux and energy
εo = αc
φo = βρε
2
s
1/ 2
o
– Parallel Potential drops (Knight [1972], Chiu [1981])
ε =
RJ ε o1/ 2
ρ
– Effects of geomagnetic field (Orens and Fedder [1978])
−ε
⎛
⎞
7εo
φ = φo ⎜ 8 − 7e ⎟ ∀ ε > 0
⎜
⎟
ε = εo + ε
⎝
⎠
φ = φo e
ε
εo
∀ ε <0
Substorm Simulation
Brief History of Neutral Wind Effects
• Killeen and Roble [1984] used the TGCM to find that neutral winds
can be driven to follow the ion convection pattern by ion drag forcing.
• Forbes and Harel [1989] modified the RCM and TGCM to include the
“effective winds” and found that these winds had a relatively small
effect on the system, but lacked a fully coupled ionospheric model.
• Deng et al. [1993] used the TIGCM to study the neutral wind
“flywheel” effect and determine that it can make significant
contributions to the FAC system during northward IMF conditions
after a geomagnetic storm.
• More recently, Peymirat et al. [2002] used the MTIE-GCM to
determine that the influence of neutral winds is limited to the auroral
zone and the produces a ~10% change in potential and a 20%
reduction in inner magnetospheric pressure.
– Ridley et al. [2003] found similar results by coupling the TIEGCM with
the BATS-R-US global MHD model of the magnetosphere.
Neutral Wind Feedback Eqs
• We can express the horizontal current in the
ionosphere as
J⊥ = σ i E +U × B
where E is the electrostatic electric field
and U × B is the neutral wind term
• Following a similar analysis as we did for the MI
coupling equations gives us
(
)
(
)
J = ∇i ∫ σ i E + σ iU × B ds
∆s
J = ∇iΣi E + ∇i ∫ σ iU × Bds
∆s
J − J W = ∇ iΣ i E
Peymirat Results
•
Neutral winds in the MTIEGCM with the SWM dynamo allow to act
like a hybrid current/voltage generator increase the polar cap potential
slightly and have significant changes near the auroral zones. A small
increase in magnetospheric pressure is seen in the region far away
from the Earth.
Ion Outflow Overview
• The magnetosphere has two main sources of
plasma
– Solar wind entry
• Borovsky et al. [1997] showed that Plasma sheet desnsity is
well correlation with solar wind density especially during
northward IMF
– Ionospheric outflow
• Numerous observations from polar orbiting satellites show
fluxes of ion like O+ at levels that correspond to plasma sheet
observations
• Two different categories of modeling ion outflow
and its impacts on the magnetosphere
– Uniform source of ions at MHD inner boundary
– Localized outflow regions
Winglee Results
•
•
Winglee [2000] used a multi-fluid
MHD description of the
magnetosphere to study the
transport of ionospheric plasma
within the magnetosphere
– Uniform O+ distribution is
accelerated out of the
ionosphere by two processes
• Centrifugal acceleration
by the fast convection
of flux tubes
• Build up of pressure
gradients between
ionosphere and
magnetotail
Tracked the location of the density
and pressure geopauses under
varying IMF conditions
1. Compute S||
S||=(E x δB/µo)||
Gagne Localized Outflow Model
Strangeway Formula:
Ion Outflow vs. Poynting Flux-CUSP
2. Dipole Map S||
to FAST altitude.
3. Compute Outflow Flux
Fi=2.14x107·S||1.265 ·f(e- Flux)
4. Map Outflow Flux back
to Inner Boundary
Rho: ρ=f(alt) (from Gallagher)
Vel: vi=Fi/ρ
Modify vi and ρ in LFM
FAST Alt.
~1.6 Re
LFM: i=1
~3.5 Re
LFM: i=5
~5 Re
Gagne Results
• On the left an image from an LFM simulation 100 minutes
into a period with steady southward IMF is contrasted with
an image on right with the MORDOR module activated
within the LFM showing localized outflow and significant
changes in the plasma sheet density.
Conclusions
• Magnetosphere – Ionosphere – Thermosphere modeling is an
active field with a long an interesting history of discovery.
• Using particle fluxes to determine conductivities has firm
physics theory, but there is room for improvement in the
methods used for getting the fluxes from MHD models.
• Thermospheric neutral wind coupling with the ionosphere and
magnetosphere is an active area of research with the next
generation of models which coupling existing regional models
together.
– Careful consideration needs to be given to making sure these couplings
preserve the conservation of mass, energy and momentum between
regions.
• Ion outflow into the magnetosphere is the newest of field and the
fledging models are promising interesting results for the future.
References I
•
•
•
•
•
•
•
•
Current system images from COMET program
Kelly, M. C., The Earth’s Ionosphere: Plasma Physics and Electrodynamics,
Academic Press, San Diego, 1989.
Spiro, R. W., P. H. Reiff, and L. J. Maher Jr., Precipitating Electron Energy
and Auroral Zone Conductances – An Empirical Model, J. Geophys. Res.,
87, 8215-8227, 1982.
Robinson, M., R. R. Vondrak, K. Miller, T. Dabbs, and D. Hardy, J.
Geophys. Res., 92, 2565-2569, 1987.
Hardy, D. A, M. S. Gussenhoven, and R. Raistrick, Statistical and Functional
Representations of the Pattern of Auroral Energy Flux, Number Flux, and
Conductivity, J. Geophys. Res., 92, 12275-12294, 1987.
Chiu, Y. T., A. L.. Newman, and J. M. Cornwall, On the structures and
Mapping of Auroral Electrostatic Potentials, J. Geophys. Res., 86, 1002910037, 1981.
Knight, S. Parallel Electric Fields, Planet. Space Sci., 21, 741-750, 1972
Orens, J. H. and J. A. Fedder, The effects of geomagnetic field aligned
potential differences on precipitating magnetospheric particles, NRL Memo.
Rep., 3573, 1978.
References II
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Killeen, T. L. and R. G. Roble, An Analysis of the High Latitude
thermospheric wind pattern calculated by a thermospheric general circulation
model, J. Geophys. Res., 89, 7509-7522, 1984.
Forbes, J. M and M. Harel, Magnetosphere-Thermosphere Coupling: An
Experiment in Interactive Modeling, J. Geophys. Res., 94, 2631-2644, 1989.
Deng, W., T. L. Killeen, A. G. Burns, R. G. Roble, J. A. Slavin, L. E.
Wharton, The Effects of Neutral Inertia on Ionospheric Currents in the HighLatitude Thermosphere Following a Geomagnetic Storm, J. Geophys. Res., 98,
7775-7790, 1993.
Peymirat, C., A. D. Richmond, and R. G. Roble, Neutral wind influence on the
electrodynamic coupling between the ionosphere and magnetosphere, J.
Geophys. Res., 107, 10.1029/2001JA900106, 2002.
Ridley, A. J., A. D. Richmond, T. I Gombosi, D. L. De Zeeuw, and C. R.
Clauer, Ionospheric Control of the Magnetospheric Configuration:
Thermospheric Neutral Winds, J. Geophys. Res., 108, 10.1029/
2002JA009464, 2003.
Winglee, R. M., Mapping of ionospheric outfows into the magnetosphere for
varying IMF conditions, J. Atm. Solar Terr. Phys., 62, 527-540, 2000.
Gagne, J. M., Implementation of Ionospheric Outflow in the LFM Global
MHD Magnetospheric Simulation, Master’s Thesis, Dartmouth Colllege,
2005.